Best match graphs (BMGs) are vertex-colored digraphs that naturally arise in mathematical phylogenetics to formalize the notion of evolutionary closest genes w.r.t. an a priori unknown phylogenetic tree. BMGs are explained by unique least resolved trees. We prove that the property of a rooted, leaf-colored tree to be least resolved for some BMG is preserved by the contraction of inner edges. For the special case of two-colored BMGs, this leads to a characterization of the least resolved trees (LRTs) of binary-explainable trees and a simple, polynomial-time algorithm for the minimum cardinality completion of the arc set of a BMG to reach a BMG that can be explained by a binary tree.
翻译:最佳匹配图(BMGs)是自然在数学植物性学中产生的脊椎色图解,以正式确定进化最接近的基因概念。BMGs的解释是独特的、分辨率最低的树。我们证明,对于某些BMG来说,根植的、叶色树的特性最难解决的是内边缘的收缩。对于两色双色BMGs的特殊案例,这导致对二进制可爆炸树中最难解决的树(LRTs)的定性,以及一种简单、多角度的算法,使BMG的弧形最小基本完成,以达到二进制树可以解释的BMG。